The set {1,2,3,4} under multiplication modulo 5.

Q: 3. Find the number of distinct permutations that can be formed your ID number.

A:

Q: 6. List all the numbers a such that you can find an a such that ax = 1 modulo 26? call such…

A: 6. For a particular n, all integers which are less than n and co-prime to n, will be invertible…

Q: The modular representation of the integer 23 with respect to the modulo 2, 3, 5 is (1,2,3) (3,2,1)…

A: the modular representation of the integer 23 with respect to the modulo 2,3,5 is it is known that…

Q: 4, and 6 if no digit is repeated in any number? a. b. repetitions are allowed?

A: We have to find the number of two digit numbers.

Q: from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 form a set containing the first four fibonacci numbers (x) that…

A: given the set

Q: Give a recursive definition for the set S ={4,7,10,13,16,19,.}.

A:

Q: Suppose each license plate in a certain state has four letters followed by two digits. The letters…

A: A license plate has four letter letters followed by two digits excluding I, O, Q, U and 0, 1, 2, 3.

Q: Let $n$ be a positive integer. Among C(2n,0),C(2n,1),..., C(2n,2n), C(2n,n) is the largest. True…

A:

Q: Compute the addition modulo operation 3+2 2 0. 1 3 O O

A:

Q: Give three elements of the equivalence class of 15 modulo 7

A:

Q: Show that the set {2/3,1/3,2/9,1/6...} is countable

A: Given set of numbers{2/3, 1/3, 2/9, 1/6...}. Here, this set of rational numbers will be proved as…

Q: a) Show that ac = bc mod cd if and only if a = b mod d

A:

Q: How many triples of integers from 2 through 16 can be formed in which the integers are in increasing…

A: Any triple of integers (i, j, k) with 2 ≤ i ≤ j ≤ k ≤ 16 can berepresented as a string of 15 – 1…

Q: How many numbers must be selected from the set {2,4,6,8,10,12,14,16,18,20} to guarantee that at…

A: Use the principle of inclusion and exclusion to solve this problem, as in next step.

Q: Suppose each license plate in a certain state has two digits, followed by two letters, followed by…

A: Given that the license plate has two digits followed by two letters again followed by two digits. Q…

Q: How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6 and 7 such that the…

A: To form a 3 digit number, we start we can not place 0 on hundreds position since that will make it a…

Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} to guarantee that at least one…

A: To find  How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} toguarantee that at least…

Q: Assume that you select digits from the set {2,3,5,7} to form a number between 20 and 700. (1) How…

A: The given set of digits is 2,3,5,7 and the range of numbers is 20 to 700. There would be 2 digit…

Q: Determine the identity element of the set N={1,2,3,..} of positive integers with addition.

A:

Q: A cosets of of 212 are اخترأحد الخیارات + 2, +1,.1 O + 1,.2 O + 4, + 1, .3 + 4, + 2, + 1 , .4 O

A: Cosets Definition: Let G be a group and let H is a nonempty subset of G. A left coset of H in G is a…

Q: How many 3-letter passwords can be made using the letters A through Z if... a) Repetition of…

A: We have to find the number of 3-letter passwords that can be made using the letters A through Z if…

Q: Assume that you are assigning one of 12 available lockers to each of the 8 players on the team. In…

A:

Q: Make a table multiplication mod 6

A:

Q: 4 If a = b (mod n), then a" = b™ (mod n) for every positive integer m.

A: It is given that  a≡b (mod n), then am≡bm (mod n) for every positive integer m. It will prove by…

Q: A1,...,A13 are thirteen different subsets of {1,2,3,4,5,6,7,8,9,10}. If each Aj has 6 elements for…

A: We are given that A1, ... , A13 are thirteen different subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.…

Q: 6. The set A = (0,1,2,3} under multiplication modulo 4

A:

Q: The Modular class of [2] under modulo 8 is O [2] = {..., -8,-4,2,4,8,...} [2]={…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 1. Let, a, = 3, az = 4 and for n 3, a, = 2a,-1+ an-2, express a, in terms of n.

A:

Q: A license plate consists of   five symbols on each​ plate, where the first two symbols are letters…

A: Fundamental principle of counting : If an event occur in m ways an corresponding to it another event…

Q: Suppose each license plate in a certain state has four letters followed by two digits. The letters…

A: When the repetition is allowed in formation the general formula for calculating the possibility is…

Q: Which pairs of the integers -11, -8, -7, -1, 0, 3, and 17 are congruent modulo 7?

A: -11≡3 (mod 7) holds  Since -11-3 = -14 is divisible by 7 and leaves remainder 0. -7≡ 0 (mod 7)…

Q: How many three digit numbers can be formed from the digits 0,1,2,3,4,5,6,7,8 and 9 such that the…

A: Given numbers are, 0,1,2,3,4,5,6,7,8 and 9 Total numbers are 10 We have to calculate the number of…

Q: Suppose each license plate in a certain state has two digits, followed by two letters, followed by…

A: To understood this, consider a problem in which there are r vacant inline spots, each of the spots…

Q: In the set {0,1,2,3,4,5}, this is the additive inverse of 4 under addition modulo 6. What is the…

A:

Q: Show that the set {2/3, 1/3, 2/9, 1/6,...} is countable

A:

Q: Find the order of 4 modulo 49.

A: Evaluate order of 4 modulo 49.

Q: 11. Define conguren ce class es for modulo 4.

A:

Q: Calculate the least residues modulo 5 of 14, 24, 34, and 44.

A:

Q: Prove (1.2), (1.3), and (1.4).  

A: (a) Let x∈A∪B So, ⇔x∈A or x∈B⇔x∈B or x∈A⇔x∈B∪A So, A∪B=B∪A

Q: A certain committee consists of 7 people. From the committee, a president, a vice president, a…

A: Solution: We need to choose a committe of a president , a vice president, a , a secretary, and a…

Q: Construct the addition and multiplication table for Z4 (Note that, both operations are mod4)

A: We have to solve given problem:

Q: A certain committee consists of 20 people. From the committee, a president, a vice-president, a…

A: Given : A certain committee consists of 20 people Now we have to choose a president, a…

Q: How many 4-digit codes can be formed from the digits 1,3,5,7, and 9 if repetition of digits is not…

A:

Q: How many strings of eight uppercase English letters are there that start and end with X, if letters…

A: In English Alphabet we have 26 letters. We have to make a string of 8 uppercase English Letters.…

Q: Which of the following sets is dlosed under the given operation? O {1, 4, 5, 7} multiplication mod 9…

A: Group. Solving ques 1 According to guidelines.

Q: 5 can be formed if the alphabet (set of avail

A: To find: Number of strings of length 5 that can be formed with {a,b,c} with last character not as b.

Q: Suppose each license plate in a certain state has one digit, followed by four letters, followed by…

A: FORMAT of number = 9AAAA9 (1 number, 4 letters, 1 number) A license plate has six spaces to be…

Q: Find the order of 5 modulo 31.

A:

Q: Write down all even permutations of {1,2,3,4} which take the element 1 to 2.

A: To write all even permutation of A={1, 2, 3, 4} that takes 1 to 2.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.